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Ideas

Explore firsthand accounts of research and questions posed by IAS scientists and scholars. From art history to string theory, from moral anthropology to the long-term fate of the universe, contributions span the last decade to the research of today.

This Institute event celebrates the work and impact of Jean Bourgain, IBM Von Neumann Professor in the School of Mathematics and member of the Faculty since 1994. Recipient of the Fields Medal and the Shaw Prize,...

Mathematics has a vital role in shaping a product’s life, from research & development to manufacturing, and from marketing to supply chain. In this public lecture, Institute Trustee Sandi Peterson and Kathy Wengel, both Princeton alumnae, ...

In the beginning of the twentieth century, the University of Göttingen was one of the top research centers for mathematics in the world. The mathematician David Hilbert was a well-established professor there, and during the winter semester of...

During a visit to the Institute in the 1970s, the mathematician John Horton Conway, then of Cambridge, spent the ten most interesting minutes of his life. Invited to deliver a talk to the undergraduate math club at Princeton, Conway made his way...

My earliest mathematical memories involve my father. One is of a walk from home to the edge of downtown Metuchen (the tiny central Jersey town where I grew up), to a little luncheonette called The Corner Confectionary. This wasn’t a frequent or...

Does beauty exist in mathematics? The question concerns mathematical objects and their relations, the real subject of verifiable proofs. Mathematicians generally agree that beauty does exist in the structural beauty of theorems and proofs, even...

Richard Schwartz, Member (2003–04) in the School of Mathematics and the Chancellor’s Professor of Mathematics at Brown University, discusses really large numbers, as well as the different sizes of infinity and the different forms of infinite space.

Topology is the branch of geometry that deals with large-scale features of shapes. One cliché is that a topologist cannot distinguish a doughnut from a coffee cup: if a coffee cup were made of rubber, one could continuously deform it to a...

How might a politics centered on spectacular black death marginalize the concerns of black women? Member Shatema Threadcraft (above) explored this question during Ideas 2017–18, in which Members explained deep ideas in under 20 minutes with no slides or chalk.

In 2012, Ahmed Almheiri, current Member in the School of Natural Sciences, coauthored a paper that confounded theoretical physicists, sparked attention from the New York Times to Scientific American, and prompted the organization of workshops and the publication of dozens of papers around the world.

Seen in the light of the antiquarian precedent, there is reason to believe that the contribution of the sciences of the past to historical research can help produce new histories. Yet, a word of caution is required.

That day in Jena, I felt the past alive in the present and understood that the legacies of the fall of communism infused current European political realities. Why else would East Germans in 2016 resurrect a protest slogan from 1989?

The correctional institution has been taken for granted and hardly made visible. An elephant in the room, it has largely been ignored by the public. In the United States, the number of people incarcerated increased more than sevenfold in four decades, reaching the impressive figure of 2.3 million inmates in the early 2010s, which made the country’s incarceration rate the highest in the world, yet without provoking a major debate.

There has been a bit of a revolution in the last few years in what we now call artificial intelligence. . . . Although we haven’t yet figured out how the brain learns, we have been able to reproduce some aspects of it.

The genealogy of modern personality cults is more complex and varied than conventionally assumed. The personal histories and interests of al-Shishakli’s advisers and cult architects suggest a source of inspiration remote from the practices of Socialist regimes. All of the available evidence indicates that the cult was informed, at least in part, by the practices of American business and political culture.

An arcane topic to most people, Syriac sources help shed a more complex light on the history of the Middle East from late antiquity to the Middle Ages. They reveal a non-imperial epoch and its rich contributions to the cultural and religious history of the region.

One of the surprising things about chaos is that it took so long for physicists to appreciate how common it is. This is despite the fact that people seem to come naturally programmed with intuition for the basic phenomenon.

Great scientists start new fields of science by making leaps in the dark. Nature decides which of the leaps is right and which is wrong. The Institute can be proud that we supported both Einstein and Joseph Weber, great scientists with their risky ventures, more than half a century before Nature proved them right and wrong.

An IAS teatime conversation in 1935 between Nathan Rosen, Boris Podolsky, and Albert Einstein, about a fundamental issue of interpretation related to entangled wave-functions, introduced an ongoing debate over quantum physics.

Long before they reached the required sensitivity to detect a merger of two neutron stars, the LIGO detectors observed a gravitational-wave signal from a black hole–black hole merger about one billion light years away.

I sometimes like to think about what it might be like inside a black hole. What does that even mean? Is it really “like” anything inside a black hole? Nature keeps us from ever knowing. But mathematics and physics make some predictions.

I read the introduction to Mathematics and Plausible Reasoning and its Chapter I standing up next to the bookshelf. It read like a novel. A cerebral one alright, which made you pay quick attention. Chapter I started out in the least orthodox way, comparing mathematical induction to a domino chain. The book endeavoured to explain not only what was mathematically true but how and why. I was hooked.

The portrait of art historian Erwin Panofsky, late Professor in the School of Historical Studies, installed in the Institute’s Historical Studies–Social Science Library, was commissioned from Philip Pearlstein in 1993. The portrait was the result of a series of coincidences that Panofsky liked to call “accidents on the highways of tradition,” this time involving a collision of at least a half-dozen vehicles of history.

I do not take the Prisoner’s Dilemma seriously as a model of evolution of cooperation, because I consider it likely that groups lacking cooperation are like dodoes, losing the battle for survival collectively rather than individually.

What is wrong with terrorism? How is terrorism chosen—picked out of all the possible political strategies? How ought we to fight against terrorism? Or better, what are the moral limits that anti-terrorists ought to recognize?

The world is emergent and always unfolding in time. Painting has difficulty representing this kind of time. The portrait tries to do that, paradoxically, by representing the individual fixed in his­torical time.

Picasso did not speak often about abstraction, but when he did, it was either to dismiss it as complacent decoration or to declare its very notion an oxymoron. But though he swore to never again go near abstraction, he could not resist testing his resolve.